Factor. 24u^2-72u+54

24u^2-72u+54

The first thing that i notice is that it can be divided through by 3

$$3(8u^2-24u+18)$$

Now I need 2 numbers that mult to 8*18      (that is positive so they must both be pos or both neg)

And they need to add to -24                        (so they must both be negative)

I am going to try and shough you what I am thinking

8*18=2*2*2*3*3*2=2*2*3      *  2*3*3       =12*12

and 12+12=24 that is great

so the numbers are -12 and -12

now replace -24u with -12u-12u

$$3[8u^2-12u-12u+18]$$

Now factorise in pairs

$$\\=3[4u(2u-3)-6(2u-3)]\\\\
=3(4u-6)(2u-3)\\\\$$

24u^2-72u+54

Testing some factors, we have

(6u - 9)(4u - 6)   ......wow.....guessed it correctly right off the bat....!!!  ......highly unusual....